Analysis of stability and bifurcations of limit cycles in Chua's circuit through the harmonic balance approach

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS: PART

Qualitative analysis of the dynamics of the time delayed Chua's circuit

IEEE TRANS. CIRCUITS SYST.

Radio Loud AGNs are Mergers

We measure the merger fraction of Type 2 radio-loud and radio-quiet active galactic nuclei at z>1 using new samples. The objects have HST images taken with WFC3 in the IR channel. These samples are compared to the 3CR sample of radio galaxies at z>1 and to a sample of non-active galaxies. We also consider lower redshift radio galaxies with HST observations and previous generation instruments (NICMOS and WFPC2). The full sample spans an unprecedented range in both redshift and AGN luminosity. We perform statistical tests to determine whether the different samples are differently associated with mergers. We find that all (92%) radio-loud galaxies at z>1 are associated with recent or ongoing merger events. Among the radio-loud population there is no evidence for any dependence of the merger fraction on either redshift or AGN power. For the matched radio-quiet samples, only 38% are merging systems. The merger fraction for the sample of non-active galaxies at z>1 is indistinguishable from radio-quiet objects. This is strong evidence that mergers are the triggering mechanism for the radio-loud AGN phenomenon and the launching of relativistic jets from supermassive black holes. We speculate that major BH-BH mergers play a major role in spinning up the central supermassive black holes in these objects.Comment: 16 pages, 6 figures, accepted for publication in the Ap

Equilibrium analysis of cellular neural networks

Cellular neural networks are dynamical systems, described by a large set of coupled nonlinear differential equations. The equilibrium point analysis is an important step for understanding the global dynamics and for providing design rules. We yield a set of sufficient conditions (and a simple algorithm for checking them) ensuring the existence of at least one stable equilibrium point. Such conditions give rise to simple constraints, that extend the class of CNN, for which the existence of a stable equilibrium point is rigorously proved. In addition, they are suitable for design and easy to check, because they are directly expressed in term of the template elements

Array of Josephson junctions with a non-sinusoidal current-phase relation as a model of the resistive transition of unconventional superconductors

An array of resistively and capacitively shunted Josephson junctions with nonsinusoidal current-phase relation is considered for modelling the transition in high-T$_c$ superconductors. The emergence of higher harmonics, besides the simple sinusoid $I_{c}\sin\phi$, is expected for dominant \emph{d}-wave symmetry of the Cooper pairs, random distribution of potential drops, dirty grains, or nonstationary conditions. We show that additional cosine and sine terms act respectively by modulating the global resistance and by changing the Josephson coupling of the mixed superconductive-normal states. First, the approach is applied to simulate the transition in disordered granular superconductors with the weak-links characterized by nonsinusoidal current-phase relation. In granular superconductors, the emergence of higher-order harmonics affects the slope of the transition. Then, arrays of intrinsic Josephson junctions, naturally formed by the CuO$_2$ planes in cuprates, are considered. The critical temperature suppression, observed at values of hole doping close to $p=1/8$, is investigated. Such suppression, related to the sign change and modulation of the Josephson coupling across the array, is quantified in terms of the intensities of the first and second sinusoids of the current-phase relation. Applications are envisaged for the design and control of quantum devices based on stacks of intrinsic Josephson junctions.Comment: Added: comparison with experiments; reference

The nuclear SED of NGC6251: a BL Lac in the center of an FR I radio galaxy

We determine the nuclear spectral energy distribution (SED) from the radio to the gamma-ray band for the FR I radio galaxy NGC6251, by using both data from the literature and analyzing HST and X-ray archival data. In the Log nu - Log nu F(nu) representation, the SED has two broad peaks, and it is remarkably similar to those of blazars. We show that the low-energy peak can be explained in terms of synchrotron radiation, while the high energy peak is most plausibly produced by inverse Compton scattering. This brings direct support to the FR I-BL Lacs unification model. We model the overall emission in the frame of a synchrotron self-Compton scenario, which well describes the SED of BL Lacs. The model parameters we obtain confirm also quantitatively the FR I-BL Lac unification model and imply a rather small viewing angle to this source (theta <~ 20deg). NGC6251 is the second radio galaxy, in addition to Centaurus A, for which a similar analysis has been performed. A significant improvement with respect to the case of Cen A is the absence of obscuration in NGC6251, which strengthens the overall result.Comment: 14 pages, 6 figures, accepted for publication in the Ap

Resistive transition in granular disordered high Tc superconductors: a numerical study

The resistive transition of granular high-Tc superconductors, characterized by either weak (YBCO-like) or strong (MgB2-like) links, occurs through a series of avalanche-type current-density rearrangements. These rearrangements correspond to the creation of resistive layers, crossing the whole specimen approximately orthogonal to the current-density direction, due to the simultaneous transition of a large number of weak links or grains. The present work shows that exact solution of the Kirchhoff equations for strongly and weakly linked networks of nonlinear resistors, with Josephson-junction characteristics, yield the subsequent formation of resistive layers within the superconductive matrix as temperature increases. Furthermore, the voltage noise observed at the transition is related to the resistive layer formation process. The noise intensity is estimated from the superposition of voltage drop elementary events related to the subsequent resistive layers. At the end of the transition, the layers mix up, the step amplitude decreases, and the resistance curve smooths. This results in the suppression of noise, as experimentally found. Remarkably, a scaling law for the noise intensity with the network size is argued. It allows us to extend the results to networks with arbitrary size and, thus, to real specimen

Neutralizing antibodies against IFN‐β in multiple sclerosis: antagonization of IFN‐β mediated suppression of MMPs

Neutralizing antibodies (NAb) against interferon‐β (IFN‐β) develop in about a third of treated multiple sclerosis patients and are believed to reduce therapeutic efficacy of IFN‐β on clinical and MRI measures. The expression of the interferon acute‐response protein, myxovirus resistance protein A (MxA) is a sensitive measure of the biological activity of therapeutically applied IFN‐β and of its reduced bioavailability due to NAb. However, MxA may not be operative in the pathogenesis of multiple sclerosis or the therapeutic effect of IFN‐β. Instead, matrix metalloproteinases (MMPs) are increased in brain tissue, CSF and blood circulation of multiple sclerosis patients and function as effector molecules in several steps of multiple sclerosis pathogenesis. One of the molecular mechanisms by which IFN‐β exerts its beneficial effect in multiple sclerosis is reduction of MMP‐9 expression and increase of its endogenous tissue inhibitor, TIMP‐1. Quantitative PCR measurements of MMP‐2 and MMP‐9, TIMP‐1 and TIMP‐2, and MxA were performed in peripheral mononuclear cells from clinically stable multiple sclerosis patients with relapsing remitting disease course after short‐term and long‐term treatment with IFN‐β. IFN‐β therapy down‐regulated the expression of MMP‐9 and abolished that of MMP‐2 in long‐term, but not short‐term treated multiple sclerosis, while levels of MxA were increased in both instances. The presence of NAb reversed these effects, i.e. led to reduced MxA and increased MMP‐2/MMP‐9 expression levels compared with NAb- patients. In contrast, expression of TIMPs in peripheral blood mononuclear cells remained unaffected by IFN‐β therapy and the presence of NAb. While MxA is able to detect the biological action and reduced bioavailability of IFN‐β on the basis of single injections, only MMP‐9 shows quantitative correlation with the NAb titre. Together with evidence that an imbalance between MMP and TIMP expression is a crucial pathogenetic feature in multiple sclerosis, these findings support the concept of a significant role of NAb in reducing the therapeutic efficacy of IFN‐

Exploring the global dynamics of networks trained through equilibrium propagation.

Equilibrium propagation is a learning technique conceived for training continuous-time recurrent neural networks. It offers some notable advantages when compared to conventional back-propagation-based algorithms and to classical design methods. From an implementation perspective, it demands only a single computational circuit. Theoretically, although it seeks to minimize a cost function, it exhibits similarities to spike- timing-dependent plasticity (STDP), rendering it, to a certain extent, biologically plausible. This paper explores the global dynamic behavior of continuous-time piecewise linear networks trained through equilibrium point propagation. We examine a network in which the target patterns are presented as external inputs rather than as initial conditions. We first show that the learning rules, which extend equilibrium propagation to gradient- like and non-symmetric networks, can be derived as a suitable approximation of Lagrangian optimization. Then, by studying a relatively simple but thoroughly significant case, we demonstrate that a detailed analysis of the equilibrium point distribution yields a profound understanding of the network’s fundamental proper- ties and provides a valuable tool for quantitatively evaluating the network’s accuracy. Compared to classical synthesis techniques, our approach, where patterns are introduced as external inputs, in most cases, circumvents the impractical task of estimating the basins of attraction for sets of multiple equilibrium points. Furthermore, preliminary extensive simulations indicate that the primary dynamic features observed in relatively small networks closely resemble those ensuring the performance and accuracy of large-scale networks